Search results for: intrinsic mode function.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3023

Search results for: intrinsic mode function.

2873 Output Regulation of Perturbed Nonlinear Systems by Nested Sliding Mode Control

Authors: Aras Adhami Mirhoseini, Mohammad J. Yazdanpanah

Abstract:

In this paper, we consider nested sliding mode control of SISO nonlinear systems, perturbed by bounded matched and unmatched uncertainties. The systems are assumed to be in strict-feedback form. A step wise procedure is introduced to obtain the controller. In each step, a continuous sliding mode controller is designed as virtual control law. Then the next step sliding surface is defined by using this virtual controller. These sliding surfaces are selected as nonlinear static functions of the system states. Finally in the last step, smooth static state feedback control law is determined such that the output reaches the desired set-point while the system is forced arbitrary close to the intersection of sliding surfaces and the states remain bounded.

Keywords: Sliding mode control, Strict-feedback form, Unmatched uncertainty, output regulation.

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2872 Learning Style and Learner Satisfaction in a Course Delivery Context

Authors: Paul David Henry

Abstract:

This paper describes the results and implications of a correlational study of learning styles and learner satisfaction. The relationship of these empirical concepts was examined in the context of traditional versus e-blended modes of course delivery in an introductory graduate research course. Significant results indicated that the visual side of the visual-verbal dimension of students- learning style(s) was positively correlated to satisfaction with themselves as learners in an e-blended course delivery mode and negatively correlated to satisfaction with the classroom environment in the context of a traditional classroom course delivery mode.

Keywords: Course delivery mode, e-blended, hybrid, learner satisfaction, learning style.

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2871 Current Drainage Attack Correction via Adjusting the Attacking Saw Function Asymmetry

Authors: Yuri Boiko, Iluju Kiringa, Tet Yeap

Abstract:

Current drainage attack suggested previously is further studied in regular settings of closed-loop controlled Brushless DC (BLDC) motor with Kalman filter in the feedback loop. Modeling and simulation experiments are conducted in a MATLAB environment, implementing the closed-loop control model of BLDC motor operation in position sensorless mode under Kalman filter drive. The current increase in the motor windings is caused by the controller (p-controller in our case) affected by false data injection of substitution of the angular velocity estimates with distorted values. Operation of multiplication to distortion coefficient, values of which are taken from the distortion function synchronized in its periodicity with the rotor’s position change. A saw function with a triangular tooth shape is studied herewith for the purpose of carrying out the bias injection with current drainage consequences. The specific focus here is on how the asymmetry of the tooth in the saw function affects the flow of current drainage. The purpose is two-fold: (i) to produce and collect the signature of an asymmetric saw in the attack for further pattern recognition process, and (ii) to determine conditions of improving stealthiness of such attack via regulating asymmetry in saw function used. It is found that modification of the symmetry in the saw tooth affects the periodicity of current drainage modulation. Specifically, the modulation frequency of the drained current for a fully asymmetric tooth shape coincides with the saw function modulation frequency itself. Increasing the symmetry parameter for the triangle tooth shape leads to an increase in the modulation frequency for the drained current. Moreover, such frequency reaches the switching frequency of the motor windings for fully symmetric triangular shapes, thus becoming undetectable and improving the stealthiness of the attack. Therefore, the collected signatures of the attack can serve for attack parameter identification via the pattern recognition route.

Keywords: Bias injection attack, Kalman filter, BLDC motor, control system, closed loop, P-controller, PID-controller, current drainage, saw-function, asymmetry.

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2870 Analysis of Euler Angles in a Simple Two-Axis Gimbals Set

Authors: Ma Myint Myint Aye

Abstract:

Any rotation of a 3-dimensional object can be performed by three consecutive rotations over Euler angles. Intrinsic rotations produce the same result as extrinsic rotations in transformation. Euler rotations are the movement obtained by changing one of the Euler angles while leaving the other two constant. These Euler rotations are applied in a simple two-axis gimbals set mounted on an automotives. The values of Euler angles are [π/4, π/4, π/4] radians inside the angles ranges for a given coordinate system and these actual orientations can be directly measured from these gimbals set of moving automotives but it can occur the gimbals lock in application at [π/2.24, 0, 0] radians. In order to avoid gimbals lock, the values of quaternion must be [π/4.8, π/8.2, 0, π/4.8] radians. The four-gimbals set can eliminate gimbals lock.

Keywords: Intrinsic rotations, extrinsic rotations, Euler rotations, rotation matrices, quaternion.

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2869 Back Stepping Sliding Mode Control of Blood Glucose for Type I Diabetes

Authors: N. Tadrisi Parsa, A. R. Vali, R. Ghasemi

Abstract:

Diabetes is a growing health problem in worldwide. Especially, the patients with Type 1 diabetes need strict glycemic control because they have deficiency of insulin production. This paper attempts to control blood glucose based on body mathematical body model. The Bergman minimal mathematical model is used to develop the nonlinear controller. A novel back-stepping based sliding mode control (B-SMC) strategy is proposed as a solution that guarantees practical tracking of a desired glucose concentration. In order to show the performance of the proposed design, it is compared with conventional linear and fuzzy controllers which have been done in previous researches. The numerical simulation result shows the advantages of sliding mode back stepping controller design to linear and fuzzy controllers.

Keywords: Back stepping, Bergman Model, Nonlinear control, Sliding mode control.

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2868 A Transfer Function Representation of Thermo-Acoustic Dynamics for Combustors

Authors: Myunggon Yoon, Jung-Ho Moon

Abstract:

In this paper, we present a transfer function representation of a general one-dimensional combustor. The input of the transfer function is a heat rate perturbation of a burner and the output is a flow velocity perturbation at the burner. This paper considers a general combustor model composed of multiple cans with different cross sectional areas, along with a non-zero flow rate.

Keywords: Thermoacoustics, dynamics, combustor, transfer function.

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2867 Predicting Protein Function using Decision Tree

Authors: Manpreet Singh, Parminder Kaur Wadhwa, Surinder Kaur

Abstract:

The drug discovery process starts with protein identification because proteins are responsible for many functions required for maintenance of life. Protein identification further needs determination of protein function. Proposed method develops a classifier for human protein function prediction. The model uses decision tree for classification process. The protein function is predicted on the basis of matched sequence derived features per each protein function. The research work includes the development of a tool which determines sequence derived features by analyzing different parameters. The other sequence derived features are determined using various web based tools.

Keywords: Sequence Derived Features, decision tree.

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2866 The Exploitation of Balancing an Inverted Pendulum System Using Sliding Mode Control

Authors: Sheren H. Salah, Ahmed Y. Ben Sasi

Abstract:

The inverted pendulum system is a classic control problem that is used in universities around the world. It is a suitable process to test prototype controllers due to its high non-linearities and lack of stability. The inverted pendulum represents a challenging control problem, which continually moves toward an uncontrolled state. This paper presents the possibility of balancing an inverted pendulum system using sliding mode control (SMC). The goal is to determine which control strategy delivers better performance with respect to pendulum’s angle and cart's position. Therefore, proportional-integral-derivative (PID) is used for comparison. Results have proven SMC control produced better response compared to PID control in both normal and noisy systems.

Keywords: Inverted pendulum (IP) proportional-integralderivative (PID), sliding mode control (SMC).

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2865 Sliding Mode Control Based on Backstepping Approach for an UAV Type-Quadrotor

Authors: H. Bouadi, M. Bouchoucha, M. Tadjine

Abstract:

In this paper; we are interested principally in dynamic modelling of quadrotor while taking into account the high-order nonholonomic constraints in order to develop a new control scheme as well as the various physical phenomena, which can influence the dynamics of a flying structure. These permit us to introduce a new state-space representation. After, the use of Backstepping approach for the synthesis of tracking errors and Lyapunov functions, a sliding mode controller is developed in order to ensure Lyapunov stability, the handling of all system nonlinearities and desired tracking trajectories. Finally simulation results are also provided in order to illustrate the performances of the proposed controller.

Keywords: Dynamic modeling, nonholonomic constraints, Backstepping, sliding mode.

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2864 Realization of Electronically Tunable Current- Mode Multiphase Sinusoidal Oscillators Using CFTAs

Authors: Prungsak Uttaphut

Abstract:

An implementation of current-mode multiphase sinusoidal oscillators is presented. Using CFTA-based lossy integrators, odd and odd/even phase systems can be realized with following advantages. The condition of oscillation and frequency of oscillation can be orthogonally tuned. The high output impedances facilitate easy driving an external load without additional current buffers. The proposed MSOs provide odd or even phase signals that are equally spaced in phase and equal amplitude. The circuit requires one CFTA, one resistor and one grounded capacitor per phase without additional current amplifier. The results of PSPICE simulations using CMOS CFTA are included to verify theory.

Keywords: multiphase sinusoidal oscillator, current-mode, CFTA, lossy integrator

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2863 Mathematical Modeling of SISO based Timoshenko Structures – A Case Study

Authors: T.C. Manjunath, Student Member, B. Bandyopadhyay

Abstract:

This paper features the mathematical modeling of a single input single output based Timoshenko smart beam. Further, this mathematical model is used to design a multirate output feedback based discrete sliding mode controller using Bartoszewicz law to suppress the flexural vibrations. The first 2 dominant vibratory modes is retained. Here, an application of the discrete sliding mode control in smart systems is presented. The algorithm uses a fast output sampling based sliding mode control strategy that would avoid the use of switching in the control input and hence avoids chattering. This method does not need the measurement of the system states for feedback as it makes use of only the output samples for designing the controller. Thus, this methodology is more practical and easy to implement.

Keywords: Smart structure, Timoshenko beam theory, Discretesliding mode control, Bartoszewicz law, Finite Element Method, State space model, Vibration control, Mathematical model, SISO.

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2862 Modeling and Simulation of Two-Phase Interleaved Boost Converter Using Open-Source Software Scilab/Xcos

Authors: Yin Yin Phyo, Tun Lin Naing

Abstract:

This paper investigated the simulation of two-phase interleaved boost converter (IBC) with free and open-source software Scilab/Xcos. By using interleaved method, it can reduce current stress on components, components size, input current ripple and output voltage ripple. The required mathematical model is obtained from the equivalent circuit of its different four modes of operation for simulation. The equivalent circuits are considered in continuous conduction mode (CCM). The average values of the system variables are derived from the state-space equation to find the equilibrium point. Scilab is now becoming more and more popular among students, engineers and scientists because it is open-source software and free of charge. It gives a great convenience because it has powerful computation and simulation function. The waveforms of output voltage, input current and inductors current are obtained by using Scilab/Xcos.

Keywords: Two-phase boost converter, continuous conduction mode, free and open-source, interleaved method, dynamic simulation.

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2861 Free Vibration Analysis of Gabled Frame Considering Elastic Supports and Semi-Rigid Connections

Authors: A. Shooshtari, A. R. Masoodi, S. Heyrani Moghaddam

Abstract:

Free vibration analysis of a gabled frame with elastic support and semi-rigid connections is performed by using a program in OpenSees software. Natural frequencies and mode shape details of frame are obtained for two states, which are semi-rigid connections and elastic supports, separately. The members of this structure are analyzed as a prismatic nonlinear beam-column element in software. The mass of structure is considered as two equal lumped masses at the head of two columns in horizontal and vertical directions. Note that the degree of freedom, allocated to all nodes, is equal to three. Furthermore, the mode shapes of frame are achieved. Conclusively, the effects of connections and supports flexibility on the natural frequencies and mode shapes of structure are investigated.  

Keywords: Natural frequency, mode shape, gabled frame, semi-rigid connection, elastic support, OpenSees software.

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2860 Selective Transverse Modes in a Diode End- Pumped Nd:Yag Pulsed Laser

Authors: M. Mohamadi, M. Mostamand, M. Moosavi, M. Soltanolkotabi

Abstract:

The output beam quality of multi transverse modes of laser, are relatively poor. In order to obtain better beam quality, one may use an aperture inside the laser resonator. In this case, various transverse modes can be selected. We have selected various transverse modes both by simulation and doing experiment. By inserting a circular aperture inside the diode end-pumped Nd:YAG pulsed laser resonator, we have obtained 00 TEM , 01 TEM , 20 TEM and have studied which parameters, can change the mode shape. Then, we have determined the beam quality factor of TEM00 gaussian mode.

Keywords: Beam shape, Transverse mode , Beam quality factor

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2859 Assessing the Function of Light and Colorin Architectural View

Authors: Gholam Hossein Naseri, Manucher Tamizi

Abstract:

Light is one of the most important qualitative and symbolic factors and has a special position in architecture and urban development in regard to practical function. The main function of light, either natural or artificial, is lighting up the environment and the constructional forms which is called lighting. However, light is used to redefine the urban spaces by architectural genius with regard to three aesthetic, conceptual and symbolic factors. In architecture and urban development, light has a function beyond lighting up the environment, and the designers consider it as one of the basic components. The present research aims at studying the function of light and color in architectural view and their effects in buildings.

Keywords: Architectural View , Color , Light

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2858 Particle Swarm Optimization and Quantum Particle Swarm Optimization to Multidimensional Function Approximation

Authors: Diogo Silva, Fadul Rodor, Carlos Moraes

Abstract:

This work compares the results of multidimensional function approximation using two algorithms: the classical Particle Swarm Optimization (PSO) and the Quantum Particle Swarm Optimization (QPSO). These algorithms were both tested on three functions - The Rosenbrock, the Rastrigin, and the sphere functions - with different characteristics by increasing their number of dimensions. As a result, this study shows that the higher the function space, i.e. the larger the function dimension, the more evident the advantages of using the QPSO method compared to the PSO method in terms of performance and number of necessary iterations to reach the stop criterion.

Keywords: PSO, QPSO, function approximation, AI, optimization, multidimensional functions.

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2857 Practical Guidelines and Examples for the Users of the TMS320C6713 DSK

Authors: Abdullah A Wardak

Abstract:

This paper describes how the correct endian mode of the TMS320C6713 DSK board can be identified. It also explains how the TMS320C6713 DSK board can be used in the little endian and in the big endian modes for assembly language programming in particular and for signal processing in general. Similarly, it discusses how crucially important it is for a user of the TMS320C6713 DSK board to identify the mode of operation and then use it correctly during the development stages of the assembly language programming; otherwise, it will cause unnecessary confusion and erroneous results as far as storing data into the memory and loading data from the memory is concerned. Furthermore, it highlights and strongly recommends to the users of the TMS320C6713 DSK board to be aware of the availability and importance of various display options in the Code Composer Studio (CCS) for correctly interpreting and displaying the desired data in the memory. The information presented in this paper will be of great importance and interest to those practitioners and developers who wants to use the TMS320C6713 DSK board for assembly language programming as well as input-output signal processing manipulations. Finally, examples that clearly illustrate the concept are presented.

Keywords: Assembly language programming, big endian mode, little endian mode, signal processing.

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2856 Statistical Approach to Basis Function Truncation in Digital Interpolation Filters

Authors: F. Castillo, J. Arellano, S. Sánchez

Abstract:

In this paper an alternative analysis in the time domain is described and the results of the interpolation process are presented by means of functions that are based on the rule of conditional mathematical expectation and the covariance function. A comparison between the interpolation error caused by low order filters and the classic sinc(t) truncated function is also presented. When fewer samples are used, low-order filters have less error. If the number of samples increases, the sinc(t) type functions are a better alternative. Generally speaking there is an optimal filter for each input signal which depends on the filter length and covariance function of the signal. A novel scheme of work for adaptive interpolation filters is also presented.

Keywords: Interpolation, basis function, over-sampling.

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2855 Investigation of Stoneley Waves in Multilayered Plates

Authors: Bing Li, Tong Lu, Lei Qiang

Abstract:

Stoneley waves are interface waves that propagate at the interface between two solid media. In this study, the dispersion characteristics and wave structures of Stoneley waves in elastic multilayered plates are displayed and investigated. With a perspective of bulk wave, a reasonable assumption of the potential function forms of the expansion wave and shear wave in nth layer medium is adopted, and the characteristic equation of Stoneley waves in a three-layered plate is given in a determinant form. The dispersion curves and wave structures are solved and presented in both numerical and simulation results. It is observed that two Stoneley wave modes exist in a three-layered plate, that conspicuous dispersion occurs on low frequency band, that the velocity of each Stoneley wave mode approaches the corresponding Stoneley wave velocity at interface between two half infinite spaces. The wave structures reveal that the in-plane displacement of Stoneley waves are relatively high at interfaces, which shows great potential for interface defects detection.

Keywords: Characteristic equation, interface waves, dispersion curves, potential function, Stoneley waves, wave structures.

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2854 Analysis of Scattering Behavior in the Cavity of Phononic Crystals with Archimedean Tilings

Authors: Yi-Hua Chen, Hsiang-Wen Tang, I-Ling Chang, Lien-Wen Chen

Abstract:

The defect mode of two-dimensional phononic crystals with Archimedean tilings was explored in the present study. Finite element method and supercell method were used to obtain dispersion relation of phononic crystals. The simulations of the acoustic wave propagation within phononic crystals are demonstrated. Around the cavity which is created by removing several cylinders in the perfect Archimedean tilings, whispering-gallery mode (WGM) can be observed. The effects of the cavity geometry on the WGM modes are investigated. The WGM modes with high Q-factor and high cavity pressure can be obtained by phononic crystals with Archimedean tilings.

Keywords: Defect mode, Archimedean tilings, phononic crystals, whispering- gallery modes.

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2853 3D Guidance of Unmanned Aerial Vehicles Using Sliding Mode Approach

Authors: M. Zamurad Shah, M. Kemal Özgören, Raza Samar

Abstract:

This paper presents a 3D guidance scheme for Unmanned Aerial Vehicles (UAVs). The proposed guidance scheme is based on the sliding mode approach using nonlinear sliding manifolds. Generalized 3D kinematic equations are considered here during the design process to cater for the coupling between longitudinal and lateral motions. Sliding mode based guidance scheme is then derived for the multiple-input multiple-output (MIMO) system using the proposed nonlinear manifolds. Instead of traditional sliding surfaces, nonlinear sliding surfaces are proposed here for performance and stability in all flight conditions. In the reaching phase control inputs, the bang-bang terms with signum functions are accompanied with proportional terms in order to reduce the chattering amplitudes. The Proposed 3D guidance scheme is implemented on a 6-degrees-of-freedom (6-dof) simulation of a UAV and simulation results are presented here for different 3D trajectories with and without disturbances.

Keywords: Unmanned Aerial Vehicles, Sliding mode control, 3D Guidance, Path following, trajectory tracking, nonlinear sliding manifolds.

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2852 AES and ECC Mixed for ZigBee Wireless Sensor Security

Authors: Saif Al-alak, Zuriati Ahmed, Azizol Abdullah, Shamala Subramiam

Abstract:

In this paper, we argue the security protocols of ZigBee wireless sensor network in MAC layer. AES 128-bit encryption algorithm in CCM* mode is secure transferred data; however, AES-s secret key will be break within nearest future. Efficient public key algorithm, ECC has been mixed with AES to rescue the ZigBee wireless sensor from cipher text and replay attack. Also, the proposed protocol can parallelize the integrity function to increase system performance.

Keywords: AES, ECC, Multi-level security, ZigBee

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2851 A Case Study to Assess the Validity of Function Points

Authors: Neelam Bawane nee' Singhal, C. V. Srikrishna

Abstract:

Many metrics were proposed to evaluate the characteristics of the analysis and design model of a given product which in turn help to assess the quality of the product. Function point metric is a measure of the 'functionality' delivery by the software. This paper presents an analysis of a set of programs of a project developed in Cµ through Function Points metric. Function points are measured for a Data Flow Diagram (DFD) of the case developed at initial stage. Lines of Codes (LOCs) and possible errors are calculated with the help of measured Function Points (FPs). The calculations are performed using suitable established functions. Calculated LOCs and errors are compared with actual LOCs and errors found at the time of analysis & design review, implementation and testing. It has been observed that actual found errors are more than calculated errors. On the basis of analysis and observations, authors conclude that function point provides useful insight and helps to analyze the drawbacks in the development process.

Keywords: Function Points, Data Flow Diagram, Lines ofCodes.

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2850 Traditional Thai Musical Instrument for Tablet Computer– Ranaad EK

Authors: Kasikrit Damkliang, Athiwat Thongnuan, Suppakit Chanlert

Abstract:

This paper proposes an architectural and graphical user interface (GUI) design of a traditional Thai musical instrument application for tablet computers for practicing “Ranaad Ek" which is a trough-resonated keyboard percussion instrument. The application provides percussion methods for a player as real as a physical instrument. The application consists of two playing modes. The first mode is free playing, a player can freely multi touches on wooden bar to produce instrument sounds. The second mode is practicing mode that guilds the player to follow percussions and rhythms of practice songs. The application has achieved requirements and specifications.

Keywords: Architectural software design, GUI; traditional Thai musical instrument, percussion instrument

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2849 Characteristic Function in Estimation of Probability Distribution Moments

Authors: Vladimir S. Timofeev

Abstract:

In this article the problem of distributional moments estimation is considered. The new approach of moments estimation based on usage of the characteristic function is proposed. By statistical simulation technique author shows that new approach has some robust properties. For calculation of the derivatives of characteristic function there is used numerical differentiation. Obtained results confirmed that author’s idea has a certain working efficiency and it can be recommended for any statistical applications.

Keywords: Characteristic function, distributional moments, robustness, outlier, statistical estimation problem, statistical simulation.

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2848 Lattice Dynamics of (ND4Br)x(KBr)1-x Mixed Crystals

Authors: Alpana Tiwari, N. K. Gaur

Abstract:

We have incorporated the translational rotational (TR) coupling effects in the framework of three body force shell model (TSM) to develop an extended TSM (ETSM). The dynamical matrix of ETSM has been applied to compute the phonon frequencies of orientationally disordered mixed crystal (ND4Br)x(KBr)1-x in (q00), (qq0) and (qqq) symmetry directions for compositions 0.10≤x≤0.50 at T=300K.These frequencies are plotted as a function of wave vector k. An unusual acoustic mode softening is found along symmetry directions (q00) and (qq0) as a result of translation-rotation coupling.

Keywords: Orientational glass, phonons, TR-coupling.

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2847 Stator-Flux-Oriented Based Encoderless Direct Torque Control for Synchronous Reluctance Machines Using Sliding Mode Approach

Authors: J. Soltani, H. Abootorabi Zarchi, Gh. R. Arab Markadeh

Abstract:

In this paper a sliding-mode torque and flux control is designed for encoderless synchronous reluctance motor drive. The sliding-mode plus PI controllers are designed in the stator-flux field oriented reference frame which is able to track the mentioned reference signals with a minimum pulsations in the state condition. In addition, with these controllers a fast dynamic response is also achieved for the drive system. The proposed control scheme is robust subject to parameters variation except to stator resistance. To solve this problem a simple estimator is used for on-line detecting of this parameter. Moreover, the rotor position and speed are estimated by on-line obtaining of the stator-flux-space vector. The effectiveness and capability of the proposed control approach is verified by both the simulation and experimental results.

Keywords: Synchronous Reluctance Motor, Direct Torque and Flux Control, Sliding Mode, Field-Oriented Frame, Encoderless.

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2846 Versatile Dual-Mode Class-AB Four-Quadrant Analog Multiplier

Authors: Montree Kumngern, Kobchai Dejhan

Abstract:

Versatile dual-mode class-AB CMOS four-quadrant analog multiplier circuit is presented. The dual translinear loops and current mirrors are the basic building blocks in realization scheme. This technique provides; wide dynamic range, wide-bandwidth response and low power consumption. The major advantages of this approach are; its has single ended inputs; since its input is dual translinear loop operate in class-AB mode which make this multiplier configuration interesting for low-power applications; current multiplying, voltage multiplying, or current and voltage multiplying can be obtainable with balanced input. The simulation results of versatile analog multiplier demonstrate a linearity error of 1.2 %, a -3dB bandwidth of about 19MHz, a maximum power consumption of 0.46mW, and temperature compensated. Operation of versatile analog multiplier was also confirmed through an experiment using CMOS transistor array.

Keywords: Class-AB, dual-mode CMOS analog multiplier, CMOS analog integrated circuit, CMOS translinear integrated circuit.

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2845 Control of a DC Servomotor Using Fuzzy Logic Sliding Mode Model Following Controller

Authors: Phongsak Phakamach

Abstract:

A DC servomotor position control system using a Fuzzy Logic Sliding mode Model Following Control or FLSMFC approach is presented. The FLSMFC structure consists of an integrator and variable structure system. The integral control is introduced into it in order to eliminated steady state error due to step and ramp command inputs and improve control precision, while the fuzzy control would maintain the insensitivity to parameter variation and disturbances. The FLSMFC strategy is implemented and applied to a position control of a DC servomotor drives. Experimental results indicated that FLSMFC system performance with respect to the sensitivity to parameter variations is greatly reduced. Also, excellent control effects and avoids the chattering phenomenon.

Keywords: Sliding mode model following control, fuzzy logic, DC servomotor.

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2844 Subclasses of Bi-Univalent Functions Associated with Hohlov Operator

Authors: Rashidah Omar, Suzeini Abdul Halim, Aini Janteng

Abstract:

The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function f ϵ A is said to be bi-univalent in the open unit disk D if both f and f-1 are univalent in D. The symbol A denotes the class of all analytic functions f in D and it is normalized by the conditions f(0) = f’(0) – 1=0. The class of bi-univalent is denoted by  The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function f is subordinate to an analytic function g if there is an analytic function w defined on D with w(0) = 0 and |w(z)| < 1 satisfying f(z) = g[w(z)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors.

Keywords: Analytic functions, bi-univalent functions, Hohlov operator, subordination.

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